Method for Computation of Local Densities for Virtual Fibers

3. The computer-implemented method of claim 2, wherein determining the plurality of orthogonal gradients comprises computing a finite-support kernel, wherein the artist parameter further comprises a smoothing radius of a density field of the finite-support kernel, and wherein the smoothing radius may be adjusted to control the virtual surface.

4. The computer-implemented method of claim 1, wherein the table of precomputed values for the artist parameter is further associated with an inverse of (2k+1) of a polynomial associated with one or more of the first vertex set.

5. The computer-implemented method of claim 1, wherein the table of precomputed values for the artist parameter is further associated with a binomial coefficient of n and k, for some integers k and n with 0≤k.

8. The computer-implemented method of claim 1, wherein the evaluations of the convolution integral for the convolved kernel are based on a local frame for a point defined by two vectors generated from two or more vertices of the first vertex set.

11. The computer system of claim 10, wherein determining the plurality of orthogonal gradients comprises computing a finite-support kernel, wherein the artist parameter further comprises a smoothing radius of a density field of the finite-support kernel, and wherein the smoothing radius may be adjusted to control the virtual surface.

12. The computer system of claim 9, wherein the table of precomputed values for the artist parameter is further associated with an inverse of a square of the artist parameter.

13. The computer system of claim 9, wherein the table of precomputed values for the artist parameter is further associated with a binomial coefficient of n and k, for some integers k and n with 0≤k.

16. A system comprising: at least one processor, and a non-transitory storage medium storing instructions, which when executed by the at least one processor, cause the system to implement the computer-implemented method of claim 1.

17. A non-transitory computer-readable storage medium storing instructions, which when executed by at least one processor of a computer system, causes the computer system to carry out the computer-implemented method of claim 1.

18. A non-transitory computer-readable medium carrying instructions, which when executed by at least one processor of a computer system, causes the computer system to carry out the computer-implemented method of claim 1.